PRP Records

Probable Primes Top 10000

(294113 PRPs in the top)


What is a PRP ?

A PRP is a probable prime number, a number that nobody knows how to prove or disprove its primality.
Here are some criterions that can be used to recognize these numbers :

- N does not have any prime factor up to 2^32.
- N cannot be trivially written into a product.
- Take 3 square-free consecutive bases such that (b1/N)=(b2/N)=(b3/N)= -1. N should be such that b1^((N-1)/2)=b2^((N-1)/2)=b3^((N-1)/2)= -1 (mod N).
- Take a prime base such that (b/N)= -1 and b<>b1<>b2<>b3. N should pass the strong test in base b.
- or more (if someone has got an idea) !!!


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1-250   251-500   501-750   751-1000   1001-1250   1251-1500   1501-1750   1751-2000   
2001-2250   2251-2500   2501-2750   2751-3000   3001-3250   3251-3500   3501-3750   3751-4000   
4001-4250   4251-4500   4501-4750   4751-5000   5001-5250   5251-5500   5501-5750   5751-6000   
6001-6250   6251-6500   6501-6750   6751-7000   7001-7250   7251-7500   7501-7750   7751-8000   
8001-8250   8251-8500   8501-8750   8751-9000   9001-9250   9251-9500   9501-9750   9751-10000   


Rank Probable prime Digits (> 50000) Who ? When ?
900110^99990-811199990Patrick De Geest02/2020
90022^332141-11307399985Enzo Doria07/2014
9003(1610172603037^8192+1610172602919^8192)/1711094812747366699983Youcef Lemsafer01/2023
90046*10^99979-7999980Robert Price03/2022
9006(3^209561+2)/72810125599978Lelio R Paula09/2013
900523827^15702+15702^2382799978Hans Havermann04/2018
90072^332085+186589799968Enzo Doria03/2016
9008(9787*2^332070-1)/93640236999959Lelio R Paula05/2015
90092^332023+19199949Lelio R Paula02/2011
9010(6271^26321-1)/627099946Serge Batalov06/2022
90117*10^99944+2799945Robert Price11/2020
90123188^28523-28523^318899931Norbert Schneider06/2023
90132^331938+7114999924Enzo Doria04/2016
90142^331932-7879599922Lelio R Paula09/2016
90152^331921+77199919Lelio R Paula01/2013
90167947^25618-25618^794799916Norbert Schneider08/2023
9017(3^209419-2)/513275599912Lelio R Paula09/2013
90182^331860-11498999900Enzo Doria05/2015
90192^331746-1165599866Lelio R Paula09/2016
902011^95891-2899861Lelio R Paula08/2016
9021(2^331694-5)/1199849Lelio R Paula10/2013
9022(3^209246+7)/6499834Lelio R Paula09/2013
902325062^9617+9617^2506299823Hans Havermann04/2018
902415^84866-5299811Lelio R Paula08/2016
902513^89600+3099810Lelio R Paula08/2016
90262^331527+10028024506599800Paul Bourdelais10/2021
902722950^22309+22309^2295099798Hans Havermann03/2018
90285^142772-3899794Lelio R Paula08/2016
9029(7482^25759-1)/748199787Serge Batalov06/2022
9030(23*2^331459+1)/47599778Lelio R Paula11/2013
90312^331416-331416+199767Robert Price10/2014
90322^331256-5799718Lelio R Paula12/2012
903328192^3443+3443^2819299714Hans Havermann03/2018
90342^331185+73799697Lelio R Paula01/2013
9035(4*10^99693+149)/999693Robert Price03/2017
90362^331154+188052799688Enzo Doria10/2016
9038(19^77951+1)/2099679Paul Bourdelais03/2010
903724354^12385+12385^2435499679Hans Havermann03/2018
90392^331110+187045999675Enzo Doria05/2016
90405*2^331075+799665Lelio R Paula08/2014
904125776^7351+7351^2577699659Hans Havermann02/2018
9042(16*10^99656-31)/399657Robert Price03/2016
9043(6059^26347-1)/605899652Serge Batalov06/2022
9044(15544^23773-1)/1554399642Serge Batalov06/2022
90462^330968+34599632Lelio R Paula09/2016
9045(2^330969+690)/299632Stefano Morozzi09/2020
90482*5^142528-799624Lelio R Paula11/2014
90472^330942+7732999624Enzo Doria05/2016
904914^86914-9999615Lelio R Paula08/2016
9050(19*2^330902+1)/7799611Lelio R Paula11/2013
905122971^21692+21692^2297199610Hans Havermann03/2018
90522^330845+7168799595Enzo Doria04/2016
9053(26667^22501-1)/2666699585Serge Batalov06/2022
9054(23*2^330770+1)/399573Lelio R Paula11/2013
905524494^11613+11613^2449499567Hans Havermann03/2018
90562^330735+841599562Lelio R Paula09/2016
90572^330720+7407199557Enzo Doria04/2016
9058(10405^24781-1)/1040499548Serge Batalov06/2022
906031^66738-299531Lelio R Paula09/2013
9059(9002^25171-1)/900199531Serge Batalov06/2022
9061(5023^26893-1)/502299527Serge Batalov06/2022
90627*3^208567+499513Lelio R Paula08/2014
9063(15881^23689-1)/1588099511Serge Batalov06/2022
9064(13*10^99508+47)/399509Robert Price01/2017
90652^330553+77999507Lelio R Paula01/2013
906615^84606-9499505Lelio R Paula08/2016
9067(10^99497+173)/399497Robert Price05/2021
90689*10^99493-4399494Robert Price09/2021
90696^127858+4799493Lelio R Paula08/2016
90705^142337+4899490Lelio R Paula08/2016
90717^117724-2099489Lelio R Paula08/2016
9072(559^36209-1)/55899479Serge Batalov06/2022
9073(13470^24091-1)/1346999477Serge Batalov06/2022
9074(29*10^99474-17)/399475Erik Branger09/2014
9075(185*10^99466-11)/399468Robert Price10/2020
9076(2^330410+2038)/299464Stefano Morozzi09/2020
9077(9*2^330407-1)/799463Lelio R Paula03/2014
9078(516*32^66077-175)/3199458Eric Chen04/2023
9079(2863^28771-1)/286299453Serge Batalov06/2022
9080(2^330373+2114)/299452Stefano Morozzi09/2020
9081(68*10^99441+7)/399443Robert Price03/2016
908210^99434+15557199435Patrick De Geest04/2020
908310^99434-12345678999434Robert Price02/2020
908410^99434-19123799434Patrick De Geest04/2020
908546^59791-45^5979199418Jean-Louis Charton01/2013
908623839^14802+14802^2383999417Hans Havermann02/2018
9087(2*10^99408+529)/999408Robert Price01/2017
9088(2^330216+3510)/299405Stefano Morozzi09/2020
908953^57646-299398Lelio R Paula09/2013
90902^330165+187002599390Enzo Doria05/2016
90917*10^99383+9799384Robert Price09/2021
90922^330142-15599383Lelio R Paula12/2012
90932^330088-11525999367Enzo Doria06/2015
909424216^12671+12671^2421699354Hans Havermann01/2018
9095Phi(200548,10)/320876999354Makoto Kamada04/2019
9096(746*10^99303+1)/999305Robert Price02/2017
90973^208107+4099293Lelio R Paula08/2016
90982^329843+21134399293Enzo Doria08/2023
9099(3939^27617-1)/393899291Serge Batalov06/2022
9100(5*2^329833-1)/36999288Lelio R Paula02/2014
91018*3^208093+599287Lelio R Paula08/2014
91025^142043+5699284Lelio R Paula08/2016
9103(13*10^99282-157)/999283Robert Price05/2021
9104(10^99284+7)/53/6799281Alfred Reich06/2021
910522*10^99275+799277Robert Price04/2016
91062^329778+187618999274Enzo Doria07/2016
9107(149557^19321-1)/(149557^139-1)99264Ryan Propper11/2023
9108(6580^25997-1)/657999259Serge Batalov06/2022
9109(2249^29611-1)/224899253Serge Batalov06/2022
9110(10^99239-13)/399239Robert Price02/2017
9111(1199^32233-1)/119899237Serge Batalov06/2022
91133^207987+6299236Lelio R Paula08/2016
9112(62*10^99235+91)/999236Robert Price07/2021
91142^329638+4999231Lelio R Paula12/2012
91157^117413-1899226Lelio R Paula08/2016
91162^329586-45890399216Enzo Doria04/2015
9117(6290^26119-1)/628999214Serge Batalov06/2022
91192^329553+10199206Lelio R Paula12/2012
9118(21297^22921-1)/2129699206Serge Batalov06/2022
91202^329551-11289799205Enzo Doria06/2014
9121(3^207925+7)/5099204Lelio R Paula09/2013
91226^127458-1799399182Enzo Doria03/2013
912327197^4428+4428^2719799166Hans Havermann10/2017
9124(46*10^99143-1)/999144Robert Price12/2014
9125(64*10^99135+161)/999136Robert Price08/2022
91267*10^99133+6999134Robert Price10/2017
9127(21701^22861-1)/2170099132Serge Batalov06/2022
912818^78968-306599127Enzo Doria03/2013
913025927^6654+6654^2592799122Hans Havermann10/2017
912987915!4+1699122Robert Price09/2019
91312^329259+18999117Lelio R Paula12/2012
91328*10^99113+3999114Robert Price01/2017
91336^127364+7799109Lelio R Paula08/2016
9134(82*10^99103+143)/999104Robert Price06/2021
9135(11414^24421-1)/1141399083Serge Batalov06/2022
9136(2^329135+1110)/299080Stefano Morozzi09/2020
9137(22089^22807-1)/2208899074Serge Batalov06/2022
9138(59*10^99069+391)/999070Robert Price03/2021
9139(797*10^99061-41)/999063Robert Price04/2022
91402^329058-28768199057Harrison Mesh06/2022
91416^127285+1399047Lelio R Paula08/2016
9142(228581#+235862)/(2^3*11*71*151)99044Makoto Morimoto10/2017
91432^329007+7328399041Enzo Doria04/2016
9144(145413^19321-1)/(145413^139-1)99030Ryan Propper11/2023
91455*3^207543-899024Lelio R Paula08/2014
9146(2^328930+570)/299018Stefano Morozzi09/2020
91472^328885+14999005Lelio R Paula12/2012
914923392^17075+17075^2339299004Hans Havermann09/2017
9148(7424^25579-1)/742399004Serge Batalov06/2022
9150(2^328879-9)/11999001Lelio R Paula10/2013
91515^141618+5498987Lelio R Paula08/2016
91522^328824+2439198986Enzo Doria10/2023
91538*10^98982+5198983Robert Price05/2017
9154(21*2^328809-1)/770998979Lelio R Paula03/2014
91552^328794-279760198977Enzo Doria04/2016
9156(88331^20011-1)/8833098972Serge Batalov06/2022
91576^127176+598963Lelio R Paula11/2014
91582*10^98961-2198962Robert Price09/2020
915924262^11989+11989^2426298960Hans Havermann09/2017
9160(60138^20707-1)/6013798958Serge Batalov06/2022
91612^328700-10970998949Enzo Doria04/2014
9162(2^328698+1810)/298948Stefano Morozzi01/2021
9163(1014^32917-1)/101398947Serge Batalov06/2022
916487771!4-12898944Robert Price11/2019
9165(4576^27031-1)/457598943Serge Batalov06/2022
9166(2^328658+3042)/298936Stefano Morozzi09/2020
9167(1933^30103-1)/193298923Serge Batalov06/2022
916846711!2-2^4671198916Robert Price09/2015
91699*7^117037+498909Lelio R Paula11/2014
9170127^47012+12698905Norbert Schneider01/2019
9171(93826^19891-1)/9382598900Serge Batalov06/2022
9172(2^328525+1250)/298896Stefano Morozzi09/2020
9173(10^98890+149)/398890Serge Batalov12/2014
917422775^21978+21978^2277598889Hans Havermann08/2017
91752^328497-21693398888Enzo Doria05/2014
91762^328487+3276998885Lelio R Paula08/2016
91773^207250-11235898884Enzo Doria06/2014
917813^88754-9098867Lelio R Paula08/2016
91792^328406+70998861Lelio R Paula02/2013
91802*10^98860-2198861Robert Price09/2020
9181(17*2^328413-1)/1617398860Lelio R Paula03/2014
91827^116976+7698857Lelio R Paula08/2016
9183(2^328378+2710)/298852Stefano Morozzi09/2020
9184(25411^22441-1)/2541098849Serge Batalov06/2022
9185(18668^23143-1)/1866798842Serge Batalov06/2022
91872^328335+115598839Lelio R Paula08/2016
91862^328333-34900398839Harrison Mesh06/2022
9189(3*2^328311+1)/598832Lelio R Paula11/2013
9188287^40210+40210^28798832Norbert Schneider11/2014
9190(2^328284+9)/132598821Lelio R Paula10/2013
9191(21*2^328258+1)/212598814Lelio R Paula11/2013
9192(28623^22171-1)/2862298806Serge Batalov06/2022
919324746^9825+9825^2474698795Hans Havermann07/2020
919426620^5143+5143^2662098793Hans Havermann07/2020
919565^54491+4898788Lelio R Paula04/2016
91963^207042+9898785Lelio R Paula08/2016
9197(2^328121+3110)/298774Stefano Morozzi09/2020
919810^98754+7338398755Patrick De Geest02/2021
92013^206977-11275698754Enzo Doria07/2014
920010^98754-4000000000198754Robert Price09/2020
919910^98754-16934398754Patrick De Geest02/2021
92027^116846-5098747Lelio R Paula08/2016
9203(19152^23059-1)/1915198740Serge Batalov06/2022
920423267^17512+17512^2326798730Hans Havermann04/2020
92052^327967-2863598728Lelio R Paula08/2016
9206707^34642+34642^70798710Norbert Schneider12/2017
9207(10771^24481-1)/1077098710Serge Batalov06/2022
92086^126850-4798709Lelio R Paula08/2016
9209(2^327886+2170)/298704Stefano Morozzi09/2020
9210(22*10^98697+47)/398698Robert Price06/2021
9211(139706^19321-1)/(139706^139-1)98696Ryan Propper11/2023
92128*6^126830-798694Lelio R Paula11/2014
921311^94770-27098693Enzo Doria08/2012
9214(2^327846+3250)/298692Stefano Morozzi01/2021
92152^327832+4398688Lelio R Paula12/2012
92162^327795+76198677Lelio R Paula02/2013
9217(2^327796+1522)/298677Stefano Morozzi09/2020
921810^98669+14741198670Patrick De Geest11/2016
922010^98669-9^(98669-1)98669Robert Price05/2016
921910^98669-10524998669Patrick De Geest11/2016
9221(7911^25309-1)/791098657Serge Batalov06/2022
92222^327671-10980198639Enzo Doria04/2014
922324398^11037+11037^2439898638Hans Havermann10/2019
92245^141090-1498618Lelio R Paula08/2016
922520^75799+4798617Lelio R Paula08/2016
9226(5452^26393-1)/545198616Serge Batalov06/2022
922728101^3226+3226^2810198597Hans Havermann07/2020
92282^327515-101798592Lelio R Paula08/2016
92296^126692+9768198586Mike Oakes04/2011
92302^327467-74198578Lelio R Paula08/2016
9231(2947^28411-1)/294698566Serge Batalov06/2022
923222713^21800+21800^2271398540Hans Havermann05/2020
9233(2^327329+9)/1998535Lelio R Paula10/2013
92347^116577-6698519Lelio R Paula08/2016
9235(3*2^327250+1)/798512Lelio R Paula11/2013
923623220^17479+17479^2322098512Hans Havermann03/2020
9237(2^327240+3798)/298509Stefano Morozzi02/2021
9238(28514^22111-1)/2851398502Serge Batalov06/2022
9239(19*2^327192+1)/27598494Lelio R Paula11/2013
92402^327162-6694598486Lelio R Paula08/2016
924130139^1852+1852^3013998484Hans Havermann02/2020
924223182^17703+17703^2318298479Hans Havermann01/2020
92434*10^98472-398473Erik Branger11/2013
924426167^5794+5794^2616798466Hans Havermann01/2020
9245(6883*2^327047-1)/7798453Lelio R Paula05/2015
9246(71*10^98446+1)/998447Serge Batalov11/2010
9247(2009^29803-1)/200898436Serge Batalov06/2022
924813^88363+9498432Lelio R Paula08/2016
924948^58543-47^5854398425Jean-Louis Charton11/2005
92506^126481+4198422Lelio R Paula08/2016


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: December, 05 2023 08:12 (Time in France)

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